Is this formula given in the exam?

No. SPM Physics papers provide no formula sheet, so this must be recalled.

Why is there a ½ in the formula?

Because the extra distance from acceleration is the area of a triangle on a velocity–time graph, whose area is ½ × base × height. The base is the time and the height is the velocity gained, giving ½at².

Do I square only the number or the unit too?

Both. (4 s)² = 16 s². Keeping the unit squared confirms that ½at² has the unit m s⁻² × s² = m, matching displacement.

What if the object starts from rest?

Then u = 0, so the first term vanishes and s = ½at². The object still travels a real distance because it is accelerating.

Second equation of motion Formula, SPM Physics

Second equation of motion

s = ut + ½at²

Not given in the exam, recall it.

What it is for

Second equation of motion is used in Force and Motion I (SPM Physics Form 4). Keep the SI units in every line of working. Force and Motion I

Symbols and SI units

Symbol	Meaning	SI unit
`s`	displacement	m
`u`	initial velocity	m s⁻¹
`a`	acceleration	m s⁻²
`t`	time	s

Rearrangements

a = 2(s − ut) / t²
u = (s − ½at²) / t

Worked example

An object starts at u = 4 m s⁻¹ and accelerates at a = 2 m s⁻² for t = 3 s. s = ut + ½at² = (4 × 3) + (½ × 2 × 3²) = 12 + 9 = 21 m.

Common trap

Square the time (t²) before multiplying, and do not forget the factor ½. Use the same sign for a as the direction of u.

Understanding the second equation of motion

The equation s = ut + ½at² gives the displacement of an object moving with uniform acceleration. Here s is the displacement in m, u is the initial velocity in m s⁻¹, a is the acceleration in m s⁻², and t is the time in s.

The displacement has two parts: the distance ut the object would cover at its starting speed, plus the extra distance ½at² gained because it is speeding up. The t² term shows that distance grows faster and faster with time.

To find acceleration: a = 2(s − ut) / t²
To find the initial velocity: u = (s − ½at²) / t

Square the time before multiplying, and never drop the factor ½.

A worked example, step by step

A cyclist starts with initial velocity u = 2 m s⁻¹ and accelerates uniformly at a = 3 m s⁻² for t = 4 s. Find the displacement.

Write the formula, then substitute with units:

s = ut + ½at²
s = (2 m s⁻¹ × 4 s) + (½ × 3 m s⁻² × (4 s)²)
s = 8 m + (½ × 3 × 16) m
s = 8 m + 24 m

So s = 32 m.

Notice the time is squared first, (4 s)² = 16 s², before multiplying by the acceleration. The answer carries the unit metre, to two significant figures.

Common mistakes and how this is tested

The classic trap is arithmetic order: you must square the time (t²) before multiplying, and you must not forget the factor ½. Other errors to watch:

Using a different sign for a than the direction of u, so the two terms should not fight unless the motion truly reverses.
Confusing displacement s with speed or velocity.
Forgetting to square the unit of time along with the number.

Examiners use calculate or determine the distance travelled, and sometimes explain why the graph of s against t is a curve. Show the full substitution so method marks are secured even if the final digit slips.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026